In the case of radio transmission, the data signals which are transmitted via the air interface have to be subjected to adaptive equalization in order to take account of the characteristics of the physical transmission channel. Multipath propagation of the transmitted data signal, which results in intersymbol interference (ISI), results in particular in difficulties in signal detection.
The multipath transmission channel between a transmitter S and a receiver E can be modeled as a transmission filter H with channel coefficients hk, as is illustrated in FIG. 1a. The transmitter S feeds transmission data or transmission symbols sk into the transmission channel, that is to say the transmission filter H. An additive noise signal nk can be taken into account by a model adder SU, and is added to the transmission symbols sk, which have been filtered with hk, at the output of the transmission filter H.
The index k denotes the discrete time, represented by time steps. The transmission signals sk which have been filtered by the transmission filter H and on which noise is superimposed are received as the received signal xk by the receiver. In this case:
                              x          k                =                                            ∑                              i                =                0                            L                        ⁢                                          h                i                            ⁢                              s                                  k                  -                  i                                                              +                      n            k                                              (        1        )            where L represents the order of the transmission channel that is modeled by the filter H. As can be seen from equation 1, this includes ISI, since xk depends not only on sk but also on sk−1, . . . ,sk−L.
The received signal values xk are known as sample values in the receiver E, and the channel impulse responses h0,h1, . . . ,hL of the channel are estimated at regular time intervals. The equalization task comprises the calculation of the transmission symbols sk from this information. The following text considers equalization by means of a Viterbi equalizer.
Viterbi equalizers are recursive MLSE (Maximum Likelihood Sequence Estimation) sequence estimators. Sequence estimation is based on finding the shortest route through a state diagram for the channel, which is known as a trellis diagram. The channel states are plotted against the discrete time k in the trellis diagram. According to the Viterbi algorithm, a transition metric is calculated for each possible transition between two states (previous state→target state), and represents a measure of the probability of that transition. The transition metrics are then added to the respective state metrics of the previous states, and the sums obtained in this way are compared. That transition whose sum of the transition metric and the metric of the previous state is a minimum is selected, and forms the extension of the path which leads in this previous state to the target state. These three operations are referred to as ACS (ADD COMPARE SELECT) operations.
The Viterbi algorithm results in the number of paths through the trellis diagram remaining constant as k increases (that is to say as the time progresses). This allows the MLSE to be solved by calculation.
The computation complexity of the Viterbi algorithm increases exponentially with L. This is due to the fact that the number of channel states in the trellis diagram is mL. In this case, m denotes the value of the data symbols being considered.
In order to increase the data rate, higher-value symbols (for example 8PSK symbols, that is to say phase shift keying with m=8) have been used increasingly in recent times instead of binary symbols (m=2). This considerably increases the computation complexity for Viterbi equalization.
Attempts have been made to cope with the increasing computation requirement by means of fast hardware data paths (coprocessors) in the hardware. These hardware modules, which are also referred to as “Viterbi supports” carry out the calculation for the ACS operations partially or entirely in hardware. One such equalizer is described, for example, in the international patent application WO 00/70614.
The decision feedback (DF) method is an algorithmic approach to reduce the computation complexity. In the DF method, the Viterbi algorithm is based on a reduced trellis diagram, that is to say a trellis diagram in which only some of the mL channel states are taken into account, rather than all of them. If the trellis diagram is reduced to mLT trellis states where LT<L, the remaining L−LT channel coefficients are used only for the calculation of the transition metrics in the reduced trellis diagram (but not for the definition of states).
However, a transition metric must always be calculated for each possible transition between two states. The transition metric is the Euclidean distance between the measured signal value xk and a reconstructed “hypothetical” signal value which is calculated in the receiver with respect to the two states (previous state, target state) which characterize the transition, taking into account the channel knowledge. The practical implementation of the calculation of the transition metrics as a function of the system concept (in particular the task distribution between hardware and software) is of critical importance for the complexity which has to be accepted for Viterbi equalization.